Some low order nonconforming mixed finite elements combined with Raviart–Thomas elements for a coupled Stokes–Darcy model
Some low order nonconforming mixed finite elements combined with Raviart–Thomas elements for a coupled Stokes–Darcy model
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DOI：
10.1007/s13160-013-0119-z
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发表时间：
2013-09
影响因子：
0.9
通讯作者：
Peiqi Huang;Jinru Chen
中科院分区：
文献类型：
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作者：
Peiqi Huang;Jinru Chen
本文讨论了求解一类耦合Stokes-Darcy方程组的数值方法。采用变形张量形式的Stokes方程描述流体运动。采用椭圆方程的混合形式描述多孔介质的渗流运动。我们提出了耦合问题的有限元方法。对于Stokes方程，速度的一个分量用Crouzeix-Raviart元或Rannacher-Turek元逼近，另一个分量用P1或Q1元逼近，压力用分段常数逼近。对于混合形式的椭圆型方程，采用最低阶三角形/四边形Raviart-Thomas元。离散网格在界面上是不匹配的。利用Boland-Nicolaides技巧证明了离散问题的inf-sup条件。此外，我们构造了一个新的插值算子，得到了所提出的有限元方法的先验误差估计。最后给出了数值例子来验证理论结果。
In this paper, we discuss numerical methods to solve a coupled Stokes–Darcy system. The deformation tensor form of Stokes equations is used to describe the fluid flow motion. The mixed form of elliptic equation is applied to describe the porous media flow motion. We propose finite element methods for the coupled problem. For Stokes equations, one component of the velocity is approximated by Crouzeix–Raviart element or Rannacher–Turek element, and the other component is approximated by conformingP1orQ1element; pressure is approximated by piecewise constants. For the mixed form of elliptic equation, the lowest order triangular/quadrilateral Raviart-Thomas element is used. The discrete mesh is nonmatching on the interface. By Boland-Nicolaides trick, the inf-sup condition of the discrete problem is proved. Moreover, we construct a new interpolation operator to derive the a priori error estimate of the proposed finite element method. Numerical examples are also given to confirm the theoretical results.